On the Transient Behavior of Conductivity Sensors

Abstract

The response characteristics of a family of conductivity cells typical of those employed in profiling instruments has been examined from a theoretical standpoint, and the conditions established under which such a cell exhibits a linear transfer function. The necessary conditions are that conductivity changes are small, and that the molecular diffusion of conductivity within the cell is negligible over times of interest. The first of these conditions is almost always satisfied, as is the second for the diffusion of salt; for conductivity changes arising from temperature, however, molecular diffusion of temperature imposes a severe limit on the linearity of the response. The analysis fully accounts for the fluid flow within the cell, and includes the effect of the internal frictional losses on the cell entry flow speed?an important effect on cell response. Numerical results of the step responses of the Neil Brown and Guildline cells are presented and those for the former closely match available experimental data over a wide range of fall speeds. Simple algebraic correlations of the numerical results allow easy prediction of the response of the Neil Brown cell and an approximate algorithm is presented, which can be applied to a wide range of cell designs.